Working Quantum Fusion: A Conserved Entanglement Ledger, Unavoidable Closure to Λ, and Control-Complexity Scaling

This triad is a three-part, internally consistent program that treats fusion as an explicitly quantum, control-limited phenomenon and reports a working architecture consistent with that view. Paper I introduces a larger framework on a conserved entanglement ledger as a global quantity and derives an unavoidable closure/rigidity condition that fixes the total capacity, yielding Λ (and related Ω fractions) from first principles within the stated axioms rather than by observational fitting. Paper II describes a fusion pathway engineered for low-dimensional steering, where LOCC-conditioned protocols act as operational controls and the working of which has been validated in protocol-gated tests, using on/off and randomised gates in the workflow. Paper III defines a control-complexity figure of merit and ranks fusion families by scaling cost, linking achievable yield to the minimal steering burden.